Answer to Question #322827 in Discrete Mathematics for Tin

Question

Let Q(x, y) denote the statement “x is the capital of y.”

What are these truth values?

a) Q(Denver, Colorado)

b) Q(Detroit, Michigan)

c) Q(Massachusetts, Boston)

d) Q(New York, New York)

Answer 1

a) Q(Denver, Colorado) = "Denver is the capital of Colorado". Therefore, the truth value is true.

b) Q(Detroit, Michigan) = "Detroit is the capital of Michigan". Therefore, the truth value is false (Lansing is the capital of Michigan ) .

c) Q(Massachusetts, Boston) = "Massachusetts is the capital of Boston" . Therefore, the truth value is false (vice versa, Boston is the capital of Massachusetts) .

d) Q(New York, New York) ="New York is the capital of New York ". Therefore, the truth value is false (Albany is the capital of New York ) .